Right. The subtle difference being that because you only sample from position i to n you only ever exchange each card exactly once. In my algo you sample from 0 to n-1 so a card exchanged in a previous round can be exchanged again. This generalises into cards early in the shuffle being exchanged more than later cards, which changes the distribution of possible outcomes.
Nerd sidenote: Because generating random numbers tends to be expensive, I had an idea once where you generate the full permutation with only a single random sample. Basically you could use something which fully enumerates a space like Gray codes[1] (you want one with a closed form solution which can arbitrarily you the nth code) then you generate one random number, multiply by the number of combinations, look up that code and decode that into the sequence of cards. I never actually got around to implementing it, but I suspect if your code lookup was fast it would be much faster than Fisher-Yates.
The use case was if you wanted to make a Monte Carlo algorithm to evaluate strategies in a card game for instance.